Growth accounting

Growth Accounting ( English growth accounting ), and growth decomposition , is a technique of neo growth theory . This enables the contribution of the individual production factors to economic growth to be determined, usually measured as gross domestic product (GDP). It was developed by Robert Merton Solow in 1957 and applied to the Solow model .

Growth accounting using the example of the Solow model

In the Solow model, the factors involved are:

${\displaystyle A}$: Technology coefficient or total factor productivity

${\displaystyle K}$: Capital stock

${\displaystyle L}$: Labor potential

In the model, the gross domestic product is calculated from a production function of the Cobb-Douglas type : ${\displaystyle Y}$

${\displaystyle Y=A\cdot K^{\alpha }L^{1-\alpha }}$ With ${\displaystyle \alpha \in (0,1)}$

A growth in GDP is thus explained by changes in the technology coefficient ( technical progress ), the accumulation of capital and the changed input of labor, for example through population growth . The exponents and correspond here to the production elasticities . In general balance in perfect competition results in that the proportion of the factor cost of GDP in each case corresponds to the production of elasticity ( English cost share theorem ). The elasticities are therefore calculated from the distribution calculation - which is only permissible if no technical restrictions prevent any combination of the production factors. ${\displaystyle \alpha }$ ${\displaystyle 1-\alpha }$

The change for all sizes can be determined from empirical data for a certain period of time . If one determines the total differential of the production function and divides it , the following equation results: ${\displaystyle Y,A,K,L}$ ${\displaystyle \Delta Y,\Delta A,\Delta K,\Delta L}$ ${\displaystyle Y}$

${\displaystyle {\frac {\Delta Y}{Y}}={\frac {\Delta A}{A}}+\alpha {\frac {\Delta K}{K}}+(1-\alpha ){\frac {\Delta L}{L}}}$

This means that the change in gross domestic product can be assigned to the individual factors. Suppose the production elasticities are calculated as and because wages were 60 percent of national income. GDP increased by 10%, labor input by 3% and net investment amounted to 8% of the capital stock: ${\displaystyle \alpha =0.4}$ ${\displaystyle 1-\alpha =0.6}$ ${\displaystyle Y}$

${\displaystyle {\frac {\Delta Y}{Y}}=0.10;\qquad {\frac {\Delta K}{K}}=0.08\Rightarrow \alpha {\frac {\Delta K}{K}}=0.032;\qquad {\frac {\Delta L}{L}}=0.03\Rightarrow (1-\alpha ){\frac {\Delta L}{L}}=0.018.}$

One can now resolve the total differential above and get:

${\displaystyle {\frac {\Delta A}{A}}={\frac {\Delta Y}{Y}}-\alpha {\frac {\Delta K}{K}}-(1-\alpha ){\frac {\Delta L}{L}}=0.10-0.032-0.018=0.05.}$

From the growth of 10 percent, the increased labor input explains 1.8 percentage points, the capital accumulation 3.2 percentage points and the technology coefficient 5 percentage points. If these percentage points are set in relation to total growth, 18 percent is formed by increased labor input, 32 percent by capital accumulation and 50 percent by total factor productivity.

Solow's calculations showed that capital accumulation and changed labor input could only explain about 20 percent of the growth, the rest initially remained unexplained as a “Solow residual”. Actually a “measure of our ignorance”, it is mostly attributed to technical progress .

Individual evidence

1. ^ Charles Hulten: Growth Accounting . In: NBER Working Paper . w15341, 2009, doi : 10.3386 / w15341 .
2. ↑ Rudiger Dornbusch, Stanley Fischer, Richard Startz: Macroeconomics , Section 3.1 Growth Accounting , Oldenbourg Verlag, 2003.
3. ^ ^{A b} Robert Merton Solow: A Contribution to the Theory of Economic Growth. In: Quarterly Journal of Economics . Volume 70, 1956, pp. 65-94 ( doi: 10.2307 / 1884513 ).
4. ^ Robert Merton Solow: Technical change and the aggregate production function . In: Review of Economics and Statistics . Volume 39, Number 3, 1957, pp. 312-320, JSTOR 1926047 .
5. ↑ Reiner Kümmel , Dietmar Lindenberger: How energy conversion drives economic growth far from the equilibrium of neoclassical economics . In: New Journal of Physics . Volume 16, number 12, 2014, 125008, doi : 10.1088 / 1367-2630 / 16/12/125008 .
6. ^ Robert U. Ayres , Benjamin Warr: Accounting for growth: the role of physical work . In: Structural Change and Economic Dynamics . Volume 16, number 2, June 2005, pp. 181-209, doi : 10.1016 / j.strueco.2003.10.003 .
7. ^ "Measure of our ignorance". M. Abramovitz: The Search for the Sources of Growth: Areas of Ignorance, Old and New . In: The Journal of Economic History . Volume 53, Number 2, June 1993, pp. 217-243, doi : 10.1017 / S0022050700012882 .
8. ^ Robert Merton Solow: Perspectives on Growth Theory. In: Journal of Economic Perspectives. 8, 1994, pp. 45-54 .: "has led to a criticism of the neoclassical model: it is a theory of growth that leaves the main factor in economic growth unexplained."